From atoms to stars: Modelling $\mathrm{H}_2$ formation and its impact on galactic evolution

TL;DR

The paper presents a sub-grid, four-phase hydrogen model embedded in AREPO to track ionised, atomic, molecular hydrogen, and stellar mass fractions within gas cells. Star formation is directly tied to the molecular content via a time-dependent mass-exchange system governed by densities and metallicities, without a fixed SF efficiency, and the relevant timescales ($\tau_{rec}$, $\tau_{cond}$, $\tau_{star}$) regulate phase transitions. Applied to a Milky Way–mass halo, the model yields a spiral galaxy with an extended gas disc, a realistic star formation history, and a molecular Kennicutt–Schmidt relation; the star-formation efficiency per free-fall time $\epsilon_{ff}$ spans $0.001\%$–$10\%$, increasing with density and metallicity. The work demonstrates that linking SF to $H_2$ can reproduce observed ISM behavior and provides a framework for comparing with more detailed SF models, while noting simplifications such as the lack of explicit radiative transfer and a simplified dust treatment that invite future refinements.

Abstract

We present a sub-grid model for star formation in galaxy simulations, incorporating molecular hydrogen ($\mathrm{H}_2$) production via dust grain condensation and its destruction through star formation and photodissociation. Implemented within the magnetohydrodynamical code AREPO, our model tracks the non-equilibrium mass fractions of molecular, ionised, and atomic hydrogen, as well as a stellar component, by solving a system of differential equations governing mass exchange between these phases. Star formation is treated with a variable rate dependent on the local $\mathrm{H}_2$ abundance, which itself varies in a complex way with key quantities such as gas density and metallicity. Testing the model in a cosmological simulation of a Milky Way-mass galaxy, we obtain a well-defined spiral structure at $z = 0$, including a gas disc twice the size of the stellar one, alongside a realistic star formation history. Our results show a broad range of star formation efficiencies per free-fall time, from as low as $0.001\%$ at high redshift to values between $0.1\%$ and $10\%$ for ages $\gtrsim 3-4 \, \mathrm{Gyr}$. These findings align well with observational estimates and simulations of a turbulent interstellar medium. Notably, our model reproduces a star formation rate versus molecular hydrogen surface densities relation akin to the molecular Kennicutt-Schmidt law. Furthermore, we find that the star formation efficiency varies with density and metallicity, providing an alternative to fixed-efficiency assumptions and enabling comparisons with more detailed star formation models. Comparing different star formation prescriptions, we find that in models that link star formation to $\mathrm{H}_2$, star formation onset is $\sim \! 500 \, \mathrm{Myr}$ later than those relying solely on total or cold gas density.

Figures (16)

• Figure 1: Physical processes responsible for transformations between the different phases. Arrows going inwards indicate that the named process increases the amount of the corresponding phase, and vice versa for arrows going outward.
• Figure 2: Comparison of the different timescales ($\tau_\mathrm{star}$, $\tau_\mathrm{cond}$, and $\tau_\mathrm{rec}$) in our model. The colour scale indicates the cell density, and the y-axis the secondary dependency of each timescale when appropriate. $\tau_\mathrm{cond}$ depends on the sum $f_a + f_m + f_i$ too (see Section \ref{['subsec:parameters']}), but for this plot we take $f_a + f_m + f_i = 1.0$.
• Figure 3: Projected stellar mass distributions, in face-on and edge-on views, for the simulation Au6_MOL at $z = 0$. The white arrows indicate the corresponding velocity field.
• Figure 4: Evolution of the SFR for the simulation Au6_MOL, computed at $z = 0$. The red and blue lines show the contribution of stars with $r \le 2 \, \mathrm{kpc}$ (mostly bulge stars) and $2 \, \mathrm{kpc} < r \le 40 \, \mathrm{kpc}$ (disc stars), respectively.
• Figure 5: Upper panel: Birth time distribution of the stars in the main sub-halo of simulation Au6_MOL at $1.6 \, \mathrm{Gyr}$. The colours indicate different birth time ranges. Lower panel: Corresponding distribution of stellar metallicities. Metal-free stars are included artificially in the leftmost bin. Metal-free stars are only formed during the first time bin ($0.0 \, \mathrm{Gyr} \leq t < 1.0 \, \mathrm{Gyr}$).